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<div class="titlepage"><div><div><h5 class="title">
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx"></a><a class="link" href="ggevx.html" title="ggevx">ggevx</a>
</h5></div></div></div>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx.prototype"></a><h6>
<a name="id812901"></a>
            <a class="link" href="ggevx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggevx.prototype">Prototype</a>
          </h6>
<p>
            There are two prototypes of <code class="computeroutput"><span class="identifier">ggevx</span></code>
            available, please see below. 
</p>
<pre class="programlisting"><span class="identifier">ggevx</span><span class="special">(</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">balanc</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">jobvl</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">jobvr</span><span class="special">,</span>
        <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">sense</span><span class="special">,</span> <span class="identifier">MatrixA</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">MatrixB</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">VectorALPHAR</span><span class="special">&amp;</span> <span class="identifier">alphar</span><span class="special">,</span>
        <span class="identifier">VectorALPHAI</span><span class="special">&amp;</span> <span class="identifier">alphai</span><span class="special">,</span> <span class="identifier">VectorBETA</span><span class="special">&amp;</span> <span class="identifier">beta</span><span class="special">,</span> <span class="identifier">MatrixVL</span><span class="special">&amp;</span> <span class="identifier">vl</span><span class="special">,</span> <span class="identifier">MatrixVR</span><span class="special">&amp;</span> <span class="identifier">vr</span><span class="special">,</span>
        <span class="identifier">int_t</span><span class="special">&amp;</span> <span class="identifier">ilo</span><span class="special">,</span> <span class="identifier">int_t</span><span class="special">&amp;</span> <span class="identifier">ihi</span><span class="special">,</span> <span class="identifier">VectorLSCALE</span><span class="special">&amp;</span> <span class="identifier">lscale</span><span class="special">,</span>
        <span class="identifier">VectorRSCALE</span><span class="special">&amp;</span> <span class="identifier">rscale</span><span class="special">,</span> <span class="identifier">Scalar</span> <span class="special">&gt;,</span> <span class="identifier">Scalar</span> <span class="special">&gt;,</span> <span class="identifier">VectorRCONDE</span><span class="special">&amp;</span> <span class="identifier">rconde</span><span class="special">,</span>
        <span class="identifier">VectorRCONDV</span><span class="special">&amp;</span> <span class="identifier">rcondv</span> <span class="special">);</span>
</pre>
<p>
          </p>
<p>
            
</p>
<pre class="programlisting"><span class="identifier">ggevx</span><span class="special">(</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">balanc</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">jobvl</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">jobvr</span><span class="special">,</span>
        <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">sense</span><span class="special">,</span> <span class="identifier">MatrixA</span><span class="special">&amp;</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">MatrixB</span><span class="special">&amp;</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">VectorALPHA</span><span class="special">&amp;</span> <span class="identifier">alpha</span><span class="special">,</span>
        <span class="identifier">VectorBETA</span><span class="special">&amp;</span> <span class="identifier">beta</span><span class="special">,</span> <span class="identifier">MatrixVL</span><span class="special">&amp;</span> <span class="identifier">vl</span><span class="special">,</span> <span class="identifier">MatrixVR</span><span class="special">&amp;</span> <span class="identifier">vr</span><span class="special">,</span> <span class="identifier">int_t</span><span class="special">&amp;</span> <span class="identifier">ilo</span><span class="special">,</span>
        <span class="identifier">int_t</span><span class="special">&amp;</span> <span class="identifier">ihi</span><span class="special">,</span> <span class="identifier">VectorLSCALE</span><span class="special">&amp;</span> <span class="identifier">lscale</span><span class="special">,</span> <span class="identifier">VectorRSCALE</span><span class="special">&amp;</span> <span class="identifier">rscale</span><span class="special">,</span>
        <span class="identifier">Scalar</span> <span class="special">&gt;,</span> <span class="identifier">Scalar</span> <span class="special">&gt;,</span> <span class="identifier">VectorRCONDE</span><span class="special">&amp;</span> <span class="identifier">rconde</span><span class="special">,</span> <span class="identifier">VectorRCONDV</span><span class="special">&amp;</span> <span class="identifier">rcondv</span> <span class="special">);</span>
</pre>
<p>
          </p>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx.description"></a><h6>
<a name="id813793"></a>
            <a class="link" href="ggevx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggevx.description">Description</a>
          </h6>
<p>
            <code class="computeroutput"><span class="identifier">ggevx</span></code> (short for $FRIENDLY_NAME)
            provides a C++ interface to LAPACK routines SGGEVX, DGGEVX, CGGEVX, and
            ZGGEVX. <code class="computeroutput"><span class="identifier">ggevx</span></code> computes
            for a pair of N-by-N complex nonsymmetric matrices (A,B) the generalized
            eigenvalues, and optionally, the left and/or right generalized eigenvectors.
          </p>
<p>
            Optionally, it also computes a balancing transformation to improve the
            conditioning of the eigenvalues and eigenvectors (ILO, IHI, LSCALE, RSCALE,
            ABNRM, and BBNRM), reciprocal condition numbers for the eigenvalues (RCONDE),
            and reciprocal condition numbers for the right eigenvectors (RCONDV).
          </p>
<p>
            A generalized eigenvalue for a pair of matrices (A,B) is a scalar lambda
            or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It
            is usually represented as the pair (alpha,beta), as there is a reasonable
            interpretation for beta=0, and even for both being zero.
          </p>
<p>
            The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
            of (A,B) satisfies A * v(j) = lambda(j) * B * v(j) . The left eigenvector
            u(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies u(j)<span class="bold"><strong>*H * A = lambda(j) * u(j)</strong></span><span class="bold"><strong>H
            * B. where u(j)</strong></span>*H is the conjugate-transpose of u(j).
          </p>
<p>
            The selection of the LAPACK routine is done during compile-time, and
            is determined by the type of values contained in type <code class="computeroutput"><span class="identifier">MatrixA</span></code>.
            The type of values is obtained through the <code class="computeroutput"><span class="identifier">value_type</span></code>
            meta-function <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">value_type</span><span class="special">&lt;</span><span class="identifier">MatrixA</span><span class="special">&gt;::</span><span class="identifier">type</span></code>. The dispatching table below illustrates
            to which specific routine the code path will be generated.
          </p>
<div class="table">
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx.dispatching_of_ggevx"></a><p class="title"><b>Table&#160;1.105.&#160;Dispatching of ggevx</b></p>
<div class="table-contents"><table class="table" summary="Dispatching of ggevx">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                    <p>
                      Value type of MatrixA
                    </p>
                  </th>
<th>
                    <p>
                      LAPACK routine
                    </p>
                  </th>
</tr></thead>
<tbody>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="keyword">float</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      SGGEVX
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="keyword">double</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      DGGEVX
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      CGGEVX
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      <code class="computeroutput"><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      ZGGEVX
                    </p>
                  </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx.definition"></a><h6>
<a name="id814166"></a>
            <a class="link" href="ggevx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggevx.definition">Definition</a>
          </h6>
<p>
            Defined in header <code class="computeroutput">boost/numeric/bindings/lapack/driver/ggevx.hpp</code>.
          </p>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx.parameters_or_requirements_on_types"></a><h6>
<a name="id814206"></a>
            <a class="link" href="ggevx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggevx.parameters_or_requirements_on_types">Parameters
            or Requirements on Types</a>
          </h6>
<div class="variablelist">
<p class="title"><b>Parameters</b></p>
<dl>
<dt><span class="term">MatrixA</span></dt>
<dd><p>
                  The definition of term 1
                </p></dd>
<dt><span class="term">MatrixB</span></dt>
<dd><p>
                  The definition of term 2
                </p></dd>
<dt><span class="term">MatrixC</span></dt>
<dd>
<p>
                  The definition of term 3.
                </p>
<p>
                  Definitions may contain paragraphs.
                </p>
</dd>
</dl>
</div>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx.complexity"></a><h6>
<a name="id814293"></a>
            <a class="link" href="ggevx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggevx.complexity">Complexity</a>
          </h6>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx.example"></a><h6>
<a name="id814319"></a>
            <a class="link" href="ggevx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggevx.example">Example</a>
          </h6>
<p>
            
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">bindings</span><span class="special">/</span><span class="identifier">lapack</span><span class="special">/</span><span class="identifier">driver</span><span class="special">/</span><span class="identifier">ggevx</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bindings</span><span class="special">;</span>

<span class="identifier">lapack</span><span class="special">::</span><span class="identifier">ggevx</span><span class="special">(</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">z</span> <span class="special">);</span>

</pre>
<p>
          </p>
<p>
            this will output
          </p>
<p>
            
</p>
<pre class="programlisting"><span class="special">[</span><span class="number">5</span><span class="special">]</span> <span class="number">0</span> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span> <span class="number">4</span> <span class="number">5</span>
</pre>
<p>
          </p>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx.notes"></a><h6>
<a name="id814602"></a>
            <a class="link" href="ggevx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggevx.notes">Notes</a>
          </h6>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.ggevx.see_also"></a><h6>
<a name="id814628"></a>
            <a class="link" href="ggevx.html#boost_numeric_bindings.reference.lapack.driver_routines.ggevx.see_also">See
            Also</a>
          </h6>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
                Originating Fortran source files <a href="http://www.netlib.org/lapack/single/sggevx.f" target="_top">sggevx.f</a>,
                <a href="http://www.netlib.org/lapack/double/dggevx.f" target="_top">dggevx.f</a>,
                <a href="http://www.netlib.org/lapack/complex/cggevx.f" target="_top">cggevx.f</a>,
                and <a href="http://www.netlib.org/lapack/complex16/zggevx.f" target="_top">zggevx.f</a>
                at Netlib.
              </li></ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2002 -2009 Rutger ter Borg, Kre&#353;imir Fresl, Thomas Klimpel,
      Toon Knapen, Karl Meerbergen<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
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